Simple, Reliable Protocol for High-Yield Solubilization of Seedless Amyloid-β Monomer

Self-assembly of the amyloid-β (Aβ) peptide to form toxic oligomers and fibrils is a key causal event in the onset of Alzheimer’s disease, and Aβ is the focus of intense research in neuroscience, biophysics, and structural biology aimed at therapeutic development. Due to its rapid self-assembly and extreme sensitivity to aggregation conditions, preparation of seedless, reproducible Aβ solutions is highly challenging, and there are serious ongoing issues with consistency in the literature. In this paper, we use a liquid-phase separation technique, asymmetric flow field-flow fractionation with multiangle light scattering (AF4-MALS), to develop and validate a simple, effective, economical method for re-solubilization and quality control of purified, lyophilized Aβ samples. Our findings were obtained with recombinant peptide but are physicochemical in nature and thus highly relevant to synthetic peptide. We show that much of the variability in the literature stems from the inability of overly mild solvent treatments to produce consistently monomeric preparations and is rectified by a protocol involving high-pH (>12) dissolution, sonication, and rapid freezing to prevent modification. Aβ treated in this manner is chemically stable, can be stored over long timescales at −80 °C, and exhibits remarkably consistent self-assembly behavior when returned to near-neutral pH. These preparations are highly monomeric, seedless, and do not require additional rounds of size exclusion, eliminating the need for this costly procedure and increasing the flexibility of use. We propose that our improved protocol is the simplest, fastest, and most effective way to solubilize Aβ from diverse sources for sensitive self-assembly and toxicity assays.

: Summary of Aβ(1-42) samples resolubilized in 10 mM NaOH. Each sample ID corresponds to a resolubilization carried out on a different date. The color schemes used for the overlays in Fig. 2 are indicated in the right-hand columns; where more than one color is listed, each color is a different repeat experiment with the same sample.

Sample ID Batch
[NaOH] Sonication HFIP Color code step Fig. 2 Table S2: Summary of Aβ(1-42) samples resolubilized in 50 mM NaOH. Each sample ID corresponds to a resolubilization carried out on a different date. The color schemes used for the overlays in Fig. 3, 4, and 8 are indicated in the right-hand columns; where more than one color is listed, each color is a different repeat experiment with the same sample.
Sample ID Batch [NaOH] Sonication HFIP Color code step   showing that seeding does not explain variation in the latter. The summary statistics in both panels are derived from the data presented in Figure 4(c) in the main text. Panel (b) uses the same color scheme as Figure 4(c), with each color indicating a different peptide sample re-solubilized on a separate occasion. Figure S3: Effect of sonication time on the self-assembly half-time and initial ThT fluorescence of Aβ(1-42) preparations re-solubilized by sonication in 50 mM NaOH prior to use in ThT assays. Self-assembly was induced by dilution of the high-pH Aβ(1-42) sample into a pH-corrected 20 mM sodium phosphate buffer (pH 8) containing 200 µM EDTA, 1 mM NaN 3 , and 20 µM ThT, at 37 o C. The initial fluorescence is given as a percentage of the final fluorescence at the end of self-assembly. The color scheme is the same as that used in Figure  7(a-c): red, no sonication; red, 0 min (no sonication); green, 5 min; blue, 30 min. Derived from the self-assembly curves presented in Figure 7(a-c) in the main text.

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S3 Removal of HMW material from 50 mM NaOH Aβ 4 preparations by ultracentrifugation 5 As described in the main text, our NS-EM and SEC experiments did not identify fibril seed 6 in Aβ(1-42) samples re-solubilized by sonication for 5 min in 50 mM NaOH, and showed 7 that attempts to remove any putative seed or oligomers had no impact on the self-assembly 8 kinetics. To complement this, and further explore the nature of the HMW contaminant that 9 eluted after cross-flow in AF4 runs, we removed the HMW material by ultracentrifugation 10 and examined the effect on the self-assembly kinetics. Firstly, an Aβ(1-42) sample was re-11 solubilized to a concentration of 1 mg/ml peptide by sonication for 5 min in 50 mM NaOH.

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An aliquot of this sample was then diluted 10× in dH 2 O to give 0.1 mg/ml Aβ(1-42) in 5 mM 13 NaOH, centrifuged at 436,000g for 1 h, and examined by AF4-MALS and ThT assays. The 14 dilution was carried out to obtain a sufficiently large volume for ultracentrifugation. As a 15 control, another aliquot from the same re-solubilized sample was diluted in the same manner, 16 and incubated in a centrifuge tube for the same period of time without ultracentrifugation.  Figure S5 shows the reverse-phase HPLC elugram of an 50 Aβ sample that had been sonicated for 5 min, and Figure S6 shows the equivalent data for an

S5 Kinetic analysis of Aβ(1-42) self-assembly mechanisms
In the main text, we analyzed the self-assembly kinetics of Aβ(1-42) samples that had been primary and secondary nucleation, with reaction order n c ≈ n 2 ≈ 2. In this section, we 82 present a more detailed kinetic analysis that supports this conclusion.

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Firstly, to more quantitatively test whether the fibrillization curves exhibited the expected early-time self-assembly kinetics, we individually fitted the same self-assembly curves that were analysed in Section 2.8 of the main text with the equation (13 -15 ) which is correct for nucleated polymerization with a directly fibril-catalyzed secondary pro- polymerization pathways, and whose precise, model-specific definitions will be given later 90 in this section. The fits, shown on semi-logarithmic axes in Figure S7, confirmed that the 91 early time self-assembly kinetics were consistent with a mechanism involving primary nucle-92 ation and a secondary fibril-generating process, with the latter becoming more important 93 as the fibril mass increases, and resulting in a straightening of the curve when viewed on 94 S13 double-logarithmic axes. Figure S7: The early-time kinetics of Aβ(1-42) preparations solubilized by sonication for 5 min in 50 mM NaOH are consistent with a mechanism involving a mixture of primary and secondary nucleation. The data shown in panels (a-g) are the same data previously presented in Figure 9 in the main text, split according to the initial Aβ (f) blue, 4.0 µM; (g) violet, 6.0 µM. In each panel, the black curve is Eq. S1, fitted to the normalized fluorescence intensities up to the half-time. Note the initial curvature, reflecting dominant primary nucleation, followed by a straightening of the curve due to increasing secondary nucleation, which results in exponential self-assembly kinetics. The model later departs from the data, as the early-time solution does not account for monomer depletion.
Statistical comparison of the ability of candidate models to fit entire time courses pro-96 vides a powerful and complementary approach to deduce the self-assembly mechanism. In  parameters shared across initial monomer concentrations. The fits are shown in Figure S8, 107 and the values of the fitted parameters and diagnostic statistics are shown in Table S3. 108 Firstly, we tested the Oosawa model (19 ). In this model, fibrils form by primary nucleation, which behaves as an n th c -order multimerization process. Fibrils then grow by stepwise addition of monomers to the fibril end, which behaves as a second-order association between a fibril and a free monomer. This model admits the exact solution (13 , 20 ) where Here, k n is the rate parameter for primary nucleation and k + is the rate parameter for 109 elongation. As shown in Figure S8  Next, we tested models that included a secondary process. Three such processes were considered: fragmentation (13 , 14 , 21 ), single-step secondary nucleation (14 ), and saturable multi-step secondary nucleation (17 , 18 ). In all three cases, the approximate solution has the same mathematical form, and the models differ only in the definitions of certain parameters.
Since fragmentation can be treated as a special case of secondary nucleation (14 , 16 ), we begin with the definitions for single-step secondary nucleation, where k 2 is the (n 2 + 1) th -order rate constant for formation of a secondary fibril nucleus 114 of effective size n 2 , at a rate also proportional to the concentration of monomers already 115 incorporated into fibrils (14 ).

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The correct solution for fragmentation can be obtained by taking the limit n 2 → 0 (in practice, setting n 2 = 10 −3 ) and substituting (13 , 14 , 21 ) (S11) where K 2 is the effective Michaelis constant for secondary nucleation, and 2 F 1 is a hyper-125 geometric function. Note that, unlike traditional Michaelis-Menten kinetics, the rate of 126 saturable secondary nucleation has an n th 2 -order rather than a linear dependence on m(t) in be small, it is significant. Comparison of the two fits using Akaike's corrected information 145 criterion (AICc) favored the latter (∆AICc = 14736, equivalent to >99.99% probability).

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Note that, in all the fits described above, the reaction orders n c and n 2 were allowed to take non-integer values, reflecting the fact that they are effective reaction orders that reflect a variety of different possible nucleation pathways involving oligomers of diverse sizes. We also used the constraint n c = n 2 , which reduces the size of parameter space and is mechanistically justified, since secondary nucleation is currently believed to involve a similar mechanism to primary nucleation (22 , 23 ). Akaike's corrected information criterion (AICc) values were calculated from the residual sum of squares (RSS) according to the relation (24 ) where N is the number of data points and K is the number of fitted parameters. The 147 likelihood of each model was proportional to exp (−AICc/2), so that the relative likelihood 148 between two models was exp (−∆AICc/2). The fitted parameter values and diagnostic 149 statistics are presented in Table S3.

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Although saturable secondary nucleation provides the best fit for the data, the fit is still 151 not perfect, with some discrepancies between the data and the fitted curves in the early 152 growth phase, particularly at lower m(0). To test whether this is caused by insufficiently 153 exponential early-time scaling in the experimental data, or simply inaccurate scaling of λ 154 and κ due to the occurrence of a more complex nucleation mechanism than the model is  (17 , 18 ). In each case, all fitted parameters are shared globally across Aβ(1-42) concentrations. The data fitted here are the same dataset that was presented in Figure 9 in the main text. The color scheme is the same across all panels, and indicates the initial Aβ(1-42) concentration: red, 1.5 µM; orange, 2.0 µM; yellow, 2.5 µM; green, 3.0 µM; cyan, 3.5 µM; blue, 4.0 µM; indigo, 5.0 µM; violet, 6.0 µM. The fitted curves are shown as black lines. The corresponding parameters are shown in Table S3. Table S3: Best-fit parameters and diagnostic statistics for the global fits in this section. In cases where an n 2 value was present, the fit was constrained such that n c = n 2 , as in Refs. (16 , 26 ). As described in the text, the value of k f was constrained to ensure that k f k + = k n k + × (10 −5.5 M) nc /(10 −8 M), as previously performed in Ref. (16 ).

Parameter Parameters from global fits Primary only
Fragmentation Secondary nucleation Saturable secondary nucleation Fig. S9(a) Fig. S9(b) Fig. S9(c) Fig. S9 freely with m(0). To reduce the size of parameter space, we set n c = n 2 = 2 for this analysis.

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Individual fitting substantially improved fit quality, indicating that the remaining discrepan-161 cies in Figure S8 Figure S8(d) are due to inaccurate scaling of λ and κ. The representative data fitted here are the same dataset that was presented in Figure 9 in the main text. The color scheme is the same across all panels, and indicates the initial Aβ

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Although the re-freezing protocol does not appear to make a difference, so long as the final 189 temperature is -80 o C, use of liquid N 2 is still recommended whenever possible.  (1-42) resolubilized to a nominal concentration of 1 mg/ml by the two main protocols examined in this study: amber, sonication for 30 min in 10 mM NaOH (final pH 10.0); and blue, sonication for 5 min in 50 mM NaOH (final pH 12.5). Note that both spectra, but particularly the pH 10.0 spectrum, exhibit enhanced absorbance at short wavelengths compared to the spectra at similar pH in panel (a), a consequence of light scattering. The light scattering in the pH 10.0 sample reflects the extensive pre-aggregation revealed by AF4-MALS, whereas the less severe light scattering in the pH 12.5 sample is probably due to the HMW species that eluted after cross-flow in the AF4-MALS runs of those samples, as large quantities of oligomers were not found to be present. Note also that the absorbance peak of the pH 12.5 sample is 20% lower than that of the same nominal concentration of tyrosine in panel (a); this is probably due to experimental variation in the quantity of Aβ(1-42) in individual vials.